**Pure and Applied Undergraduate Texts**

Volume: 2;
2002;
788 pp;
Hardcover

MSC: Primary 65;

Print ISBN: 978-0-8218-4788-6

Product Code: AMSTEXT/2

List Price: $94.00

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MAA Member Price: $84.60

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**Electronic ISBN: 978-1-4704-1115-2
Product Code: AMSTEXT/2.E**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

# Numerical Analysis: Mathematics of Scientific Computing, Third Edition

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*David Kincaid; Ward Cheney*

This book introduces students with diverse backgrounds to various types of
mathematical analysis that are commonly needed in scientific computing.
The subject of numerical analysis is treated from a mathematical point of
view, offering a complete analysis of methods for scientific computing
with appropriate motivations and careful proofs.

In an engaging and informal style, the authors demonstrate that many
computational procedures and intriguing questions of computer science
arise from theorems and proofs. Algorithms are presented in pseudocode, so
that students can immediately write computer programs in standard
languages or use interactive mathematical software packages.

This book occasionally touches upon more advanced topics that are not
usually contained in standard textbooks at this level.

An instructor's manual for this title is available electronically. Please
send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate and graduate students interested in applied mathematics and scientific computing.

#### Reviews & Endorsements

This text offers a thorough and elegant presentation of basic topics in numerical analysis. ... the text is skillfully written, by authors who are among the best in the field. Throughout, the presentation shows the unique insights that each brings to the subject. In all, it is an enjoyable text to use.

-- Bulletin of Mathematics Books and Computer Science

#### Table of Contents

# Table of Contents

## Numerical Analysis: Mathematics of Scientific Computing, Third Edition

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Preface ix10 free
- Numerical Analysis: What Is It? 116 free
- 1 Mathematical Preliminaries 318
- 2 Computer Arithmetic 3752
- 3 Solution of Nonlinear Equations 7388
- 4 Solving Systems of Linear Equations 139154
- 4.0 Introduction 139154
- 4.1 Matrix Algebra 140155
- 4.2 LU and Cholesky Factorizations 149164
- 4.3 Pivoting and Constructing an Algorithm 163178
- 4.4 Norms and the Analysis of Errors 186201
- 4.5 Neumann Series and Iterative Refinement 197212
- 4.6 Solution of Equations by Iterative Methods 207222
- 4.7 Steepest Descent and Conjugate Gradient Methods 232247
- 4.8 Analysis of Roundoff Error in the Gaussian Algorithm 245260

- 5 Selected Topics in Numerical Linear Algebra 254269
- 5.0 Review of Basic Concepts 254269
- 5.1 Martix Eigenvalue Problem: Power Method 257272
- 5.2 Schur's and Gershgorin's Theorems 265280
- 5.3 Orthogonal Factorizations and Least-Squares Problems 273288
- 5.4 Singular-Value Decomposition and Pseudo inverses 287302
- 5.5 QR-Algorithm of Francis for the Eigenvalue Problem 298313

- 6 Approximating Functions 308323
- 6.0 Introduction 308323
- 6.1 Polynomial Interpolation 308323
- 6.2 Divided Differences 327342
- 6.3 Hermite Interpolation 338353
- 6.4 Spline Interpolation 349364
- 6.5 B-Splines: Basic Theory 366381
- 6.6 B-Splines: Applications 377392
- 6.7 Taylor Series 388403
- 6.8 Best Approximation: Least-Squares Theory 392407
- 6.9 Best Approximation: Chebyshev Theory 405420
- 6.10 Interpolation in Higher Dimensions 420435
- 6.11 Continued Fractions 438453
- 6.12 Trigonometric Interpolation 445460
- 6.13 Fast Fourier Transform 451466
- 6.14 Adaptive Approximation 460475

- 7 Numerical Differentiation and Integration 465480
- 7.1 Numerical Differentiation and Richardson Extrapolation 465480
- 7.2 Numerical Integration Based on Interpolation 478493
- 7.3 Gaussian Quadrature 492507
- 7.4 Romberg Integration 502517
- 7.5 Adaptive Quadrature 507522
- 7.6 Sard's Theory of Approximating Functionals 513528
- 7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula 519534

- 8 Numerical Solution of Ordinary Differential Equations 524539
- 8.0 Introduction 524539
- 8.1 The Existence and Uniqueness of Solutions 524539
- 8.2 Taylor-Series Method 530545
- 8.3 Runge-Kutta Methods 539554
- 8.4 Multistep Methods 549564
- 8.5 Local and Global Errors: Stability 557572
- 8.6 Systems and Higher-Order Ordinary Differential Equations 565580
- 8.7 Boundary-Value Problems 572587
- 8.8 Boundary-Value Problems: Shooting Methods 581596
- 8.9 Boundary-Value Problems: Finite-Differences 589604
- 8.10 Boundary-Value Problems: Collocation 593608
- 8.11 Linear Differential Equations 597612
- 8.12 Stiff Equations 608623

- 9 Numerical Solution of Partial Differential Equations 615630
- 9.0 Introduction 615630
- 9.1 Parabolic Equations: Explicit Methods 615630
- 9.2 Parabolic Equations: Implicit Methods 623638
- 9.3 Problems Without Time Dependence: Finite-Differences 629644
- 9.4 Problems Without Time Dependence: Galerkin Methods 634649
- 9.5 First-Order Partial Differential Equations: Characteristics 642657
- 9.6 Quasilinear Second-Order Equations: Characteristics 650665
- 9.7 Other Methods for Hyperbolic Problems 660675
- 9.8 Multigrid Method 667682
- 9.9 Fast Method s for Poisson's Equation 676691

- 10 Linear Programming and Related Topics 681696
- 11 Optimization 711726
- 11.0 Introduction 711726
- 11.1 One-Variable Case 712727
- 11.2 Descent Methods 716731
- 11.3 Analysis of Quadratic Objective Functions 719734
- 11.4 Quadratic-Fitting Algorithms 721736
- 11.5 Nelder-Mead Algorithm 722737
- 11.6 Simulated Annealing 723738
- 11.7 Genetic Algorithms 724739
- 11.8 Convex Programming 725740
- 11.9 Constrained Minimization 726741
- 11.10 Pareto Optimization 727742

- Appendix A: An Overview of Mathematical Software 731746
- Bibliography 745760
- Index 771786
- Back Cover Back Cover1804